New visible polarization data combined with existing IR and FIR polarization data are used to study how the magnetic field threading the filamentary molecular cloud GF 9 connects to larger structures in its general environment. When visible and NIR polarization data are combined, no evidence is found for a plateau in the polarization above extinction AV~1.3, as seen in dark clouds in Taurus. This lack of saturation effect suggests that even in the denser parts of GF 9 magnetic fields can be probed. The visible polarization is smooth and has a well-defined orientation. In the core region, the IR and FIR data are also well defined, but each with a different direction. A multiscale analysis of the magnetic field shows that on the scale of a few times the mean radial dimension of the molecular cloud, it is as if the magnetic field were ``blind'' to the spatial distribution of the filaments, while on smaller scales in the core region, multiwavelength polarimetry shows a rotation of the magnetic field lines in these denser phases. Finally, the Chandrasekhar and Fermi method is used to evaluate the magnetic field strength, indicating that the core region is approximately magnetically critical. A global interpretation suggests that in the core region an original poloidal field could have been twisted by a rotating elongated (core+envelope) structure. There is no evidence for turbulence, and ambipolar diffusion does not seem to be effective at the present time.